Study On Online Sequential Extreme Learning Machine And Its Application

Extreme learning machine is a single hidden layer feedforward neural network.The original ELM belongs to a batch learning algorithm,in which the data are fully available when the training process starts.However,in many real-world applications,data always come continuously and might never have an end.For these online applications,the Online Sequential Extreme learning machine(OS-ELM)is proposed.It can process the data arriving one by one or block by block sequentially,and has good generalization ability and fast learning speed.We make some improvements from the two aspects of non-Gaussian noise robustness and the optimal hidden layer structure in this paper.Besides,we apply the proposed algorithms on the channel equalization scenario of the OFDM system.The detailed content is as follows:(1)The Mean Squared Error(MSE)criterion is adopted to construct the cost function in the OS-ELM.Since this criterion only considers the second-order statistics of the data,it will perform poorly when dealing with non-Gaussian distributed data.In this paper,we develop a new online sequential extreme learning machine algorithm based on robust recursive least squares,namely RR-OSELM.We employ the Maximum Correntropy Criterion to construct the cost function,and utilize the half-quadratic optimization method to transform the cost function into a quadratic problem,so that we can derive the recursive form of the output weights.The theoretical proof on the convergence of the proposed scheme is given and we make some experiments.The results show that the proposed algorithm has good robustness when the expected data is contaminated by non-Gaussian noise.(2)The number of hidden nodes have to be manually and randomly chosen in the OS-ELM.Too large hidden layer will cause over-fitting problems,but too small will reduce the estimation accuracy.In order to get the optimal structure of the hidden layer automatically,we develop a new online sequential extreme learning machine based on sparse recursive least squares(S-OSELM).By adding the l₀-norm and l₁-norm regularization penalty terms into the cost function,we can obtain the sparse solution of the output weights.And we adopt the sub-gradient method and finally get the updating formula of the output weight.At the same time,in order to avoid the improper regularization parameter that reduces the accuracy,we propose an adaptive tuning method about the regularization parameter.Besides,the convergence of the S-OSELM is theoretically proved.The simulation results show that the proposed S-OSELM-l₀ and S-OSELM-l₁ algorithms not only have a structure with fewer hidden nodes,but also gain a higher accuracy.(3)When the Orthogonal Frequency Division Multiplexing(OFDM)system passes through the high-power amplifier(HPA)and fading channel,the nonlinear distortion and multipath effects will greatly affect the quality of the communication system.Most of the existing neural network-based OFDM channel equalization methods require offline training of the channel model in advance.When the real channel is different from the previous one,they will perform badly.To overcome these limitations,we propose an online sequential extreme learning machine-based channel equalization scheme.Simulation results show that the proposed method can resist the nonlinear distortion and multipath fading effect,and can obtain a lower bit error rate compared with the traditional methods for channel equalization.